Question: User: $-2x+3y=-5$ and $-x+4y=5$.
1. **State the problem:** Solve the system of linear equations:
$$-2x + 3y = -5$$
$$-x + 4y = 5$$
2. **Formula and rules:** We can solve this system using substitution or elimination. Here, we'll use elimination.
3. **Step 1: Multiply the second equation by 2 to align coefficients of $x$:**
$$2(-x + 4y) = 2(5)$$
$$-2x + 8y = 10$$
4. **Step 2: Subtract the first equation from this new equation:**
$$(-2x + 8y) - (-2x + 3y) = 10 - (-5)$$
Simplify:
$$-2x + 8y + 2x - 3y = 10 + 5$$
$$5y = 15$$
5. **Step 3: Solve for $y$:**
$$y = \frac{15}{5}$$
$$y = 3$$
6. **Step 4: Substitute $y=3$ into the second original equation:**
$$-x + 4(3) = 5$$
$$-x + 12 = 5$$
7. **Step 5: Solve for $x$:**
$$-x = 5 - 12$$
$$-x = -7$$
$$x = 7$$
**Final answer:**
$$x = 7, \quad y = 3$$